I'm a web developer looking into some basic statistics -- pardon me if I am using the wrong jargon. :)
- I have 2 populations (A and B; each have about 10,000 observations)
- For each population I know the size, the mean and the standard deviation
- I have one "lost" observation
- I know for sure that this observation belongs either in population A or in population B. It cannot co-exist in both populations.
Is it possible to determine the probabilities that the observation belongs in population A or population B? I would then compare each probability to determine which case is more likely.
I would prefer not to make an assumption about the distribution of each population. However, if necessary, it would be fair to assume that the populations are normally distributed.
In case it helps, I have some sample data available:
- observation x of interest:
- population A mean:
10061, standard deviation:
- population B mean:
9939, standard deviation:
What is the chance for observation x to be in population A? What is the chance for observation x to be in population B?
Note that I realize that the means and standard deviations of both populations are very similar. I don't mind if the probabilities are very similar too. This is just an example observation.